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Problem #453

A cubic form
 Public ★(x4) 01/10/18 by sinan 8xp Math 80.0%

Let D(x,y,z) = x3 + y3 + z3 - 3*x*y*z

It can be proven that for any integers x1,y1,z1,x2,y2,z2 there exist integers x3,y3,z3 such that:
D(x1,y1,z1)*D(x2,y2,z2) = D(x3,y3,z3)

Let N be the number of (x3,y3,z3) triples of the form x3≤y3≤z3 for D(x1,y1,z1)*D(x2,y2,z2) = D(x3,y3,z3).

Find the N and the sum of all z3 values for D(34040,34238,35404)*D(34551,34564,34567).

Example: 12,548 for D(1,2,3)*D(11,12,13)

[My timing: <1m]

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